arXiv:0904.4259

Disproofs of Bell, GHZ, and Hardy Type Theorems and the Illusion of Entanglement

Joy Christian

Published Apr 28, 2009• 12 citations

Abstract

An elementary topological error in Bell's representation of the EPR elements of reality is identified. Once recognized, it leads to a topologically correct local-realistic framework that provides exact, deterministic, and local underpinning of at least the Bell, GHZ-3, GHZ-4, and Hardy states. The correlations exhibited by these states are shown to be exactly the classical correlations among the points of a 3 or 7-sphere, both of which are closed under multiplication, and hence preserve the locality condition of Bell. The alleged non-localities of these states are thus shown to result from misidentified topologies of the EPR elements of reality. When topologies are correctly identified, local-realistic completion of any arbitrary entangled state is always guaranteed in our framework. This vindicates EPR, and entails that quantum entanglement is best understood as an illusion.

DOI: 10.48550/arxiv.0904.4259

Related papers

Restoring Local Causality and Objective Reality to the Entangled Photons

Joy Christian

Unlike our basic theories of space and time, quantum mechanics is not a locally causal theory. Moreover, it is widely believed that any hopes of restoring local causality within a realistic theory have been undermined by Bell's theorem and its supporting experiments. By contrast, we provide a strictly local, deterministic, and realistic explanation for the correlations observed in two such supporting experiments, performed independently at Orsay and Innsbruck. To this end, a pair of local variables is constructed to simulate detections of photon polarizations at various angles, chosen freely by Alice and Bob. These generate purely random outcomes, A = +1 or -1 and B = +1 or -1, occurring within a parallelized 3-sphere. These outcomes do not depend on the contexts of measurements, but are determined entirely by the randomly chosen initial orientation of the 3-sphere. When they are compared, however, the correlation between them turn out to be exactly equal to -cos2(alpha - beta), with the corresponding CHSH inequality violated for the polarization angles alpha, alpha', beta, and beta' in precisely the manner predicted by quantum mechanics. The key ingredient in our explanation is the topology of the 3-sphere, which remains closed under multiplication, thus preserving the locality condition of Bell. It allows us to model the physical space as a 3-sphere, and reveals that the illusion of quantum nonlocality in the present case stems from a twist in the Hopf fibration of the 3-sphere.

arXiv:1106.0748Jun 3, 20117 citations

What Really Sets the Upper Bound on Quantum Correlations?

Joy Christian

The discipline of parallelization in the manifold of all possible measurement results is shown to be responsible for the existence of all quantum correlations, with the upper bound on their strength stemming from the maximum of possible torsion within all norm-composing parallelizable manifolds. A profound interplay is thus uncovered between the existence and strength of quantum correlations and the parallelizability of the spheres S^0, S^1, S^3, and S^7 necessitated by the four real division algebras. In particular, parallelization within a unit 3-sphere is shown to be responsible for the existence of EPR and Hardy type correlations, whereas that within a unit 7-sphere is shown to be responsible for the existence of all GHZ type correlations. Moreover, parallelizability in general is shown to be equivalent to the completeness criterion of EPR, in addition to necessitating the locality condition of Bell. It is therefore shown to predetermine both the local outcomes as well as the quantum correlations among the remote outcomes, dictated by the infinite factorizability of points within the spheres S^3 and S^7. The twin illusions of quantum entanglement and non-locality are thus shown to stem from the topologically incomplete accountings of the measurement results.

arXiv:1101.1958Jan 10, 201110 citations

Refutation of Some Arguments Against my Disproof of Bell's Theorem

Joy Christian

In a couple of recent preprints Moldoveanu has suggested that there are errors in my disproof of Bell's theorem. Here I show that this claim is false. In particular, I show that my local-realistic framework is incorrectly and misleadingly presented in both of his preprints. In addition there are a number of serious mathematical and conceptual errors in his discussion of my framework. For example, contrary to his claim, my framework is manifestly non-contextual. In particular, quantum correlations are understood within it as purely topological effects, not contextual effects.

arXiv:1110.5876Oct 19, 20113 citations

Beyond Bell’s theorem: realism and locality without Bell-type correlations

F. De Zela

The long-lasting view of entanglement as the characteristic trait of quantum mechanics has been recently challenged by experimental demonstrations of non-quantum entanglement. This motivates a review of the meaning of Bell violations, which have been widely taken to prove the impossibility of a realistic interpretation of quantum mechanics and as a manifestation of its non-local character. This work provides new theoretical evidence for the need of reviewing the meaning of Bell violations, especially when they occur outside the quantum framework. We present a local-realistic model that reproduces quantum predictions concerning Bell tests. We claim that local-realism is fully compatible with correlations that are not of the Bell type and therefore lie outside the scope of Bell's theorem. Most experimental Bell tests involve either spin vectors spanning the Bloch sphere or Stokes vectors spanning the Poincaré sphere. A suitable statistical tool that allows assessing correlations between vectors is given by inner-product-type correlations. Using them, it is possible to reproduce quantum predictions for all Bell states, thereby explaining experimental results of Bell tests within a local-realistic framework.

Scientific ReportsOct 31, 20176 citations

EPR, Bell, GHZ, and Hardy theorems, and quantum mechanics

M. Socolovsky

We review the theorems of Einstein-Podolsky-Rosen (EPR), Bell, Greenberger-Horne-Zeilinger (GHZ), and Hardy, and present arguments supporting the idea that quantum mechanics is a complete, causal, non local, and non separable theory.

arXiv:quant-ph/0508077Aug 9, 20050 citations

Are quantum correlations local elements of reality? A Bell inequality to test this

Michael Seevinck

We show, using a Bell inequality argument, that quantum correlations cannot be regarded as local elements of reality. It is well known since the work of J.S. Bell, that one cannot have locally preexistent values for all physical quantities, whether they are deterministic or stochastic. The Bell inequality argument we present here shows this is also impossible for correlations among subsystems of an individual isolated composite system. Thus there is no philosophical difference with respect to questions of locality and realism between correlations on the one hand and values of quantities on the other hand that could allow one to have a different view about their ontological status. Neither of them can be used to build up a world consisting of some local realistic structure. This argument has an important advantage over others who use so-called Greenberger-Horne-Zeilinger and Hardy type arguments because it does not need perfect correlations but only statistical correlations. It can therefore easily be tested in currently feasible experiments using four particle entanglement.

Aug 23, 20050 citations